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sir! i'm struggling with precalculus, can you send some precalculus notes, and you pls explain how to find a range of function.
All functions have what is called a domain and a range.
The domain where the function is defined. Just think of it like property - the domain of land that is relevant to you is how much you own. The domain of a function is the values on which it is defined.
On your property, you might have a wide range of things at which to look, but they would all be things that were on your domain. Well, the range of a function is the possible values of the function over the domain that was given.
Now I have a hard time understanding what was said without an example, so I've included a couple.
1. If f(x)=x^2 is the function, the domain is all that can be seen to be put into the function, which is all x. The range is what comes out. Note that no matter what we put in, we always get a non-negatve, so the range is [0,∞). The [ is because we inclue 0 and the ) is because ∞ can't be included.
2. Another function g(x) would be g(x)=x²-4 on [0,3].
The domain would be the [0,3] and the range would be [-4,5]. Again, [ , ] includes the endpoint whereas ( , ) does not.
If the domain were (1,5), the range would be (-3,21).
If the domain were [2,5) (only include the 2, but not the 5, just everything as close as you can get to 5), the range would be [0,21).
In summary, to find the range, take the points in the domain and see where they come out when the function is applied. This will tell you the range. [,] includes endpoint, (,) does not. Note that ∞ is never included (probably since it can't be reached).
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